()()main and l?anae. State the domain and range of the following relation. Is the relation a function? {(2,-3), (4, 6), (3, -1), (6, 6), (2, 3)}

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1 V.. ()pertie~ ()f r=un(;ti()n~ ()()main and l?anae The set of all the starting points is called "the " and the set of all the ending points is called "the." The is what ou start with; the is what ou end up with. The is the 's; the is the 's. State the and of the following relation. s the relation a function? {(2,3), (4, 6), (3, 1), (6, 6), (2, 3)} o : {2, 3, 4, 6} o: {3, 1, 3, 6} o Since = 2 gives me two possible destinations (2,3) and (2,3) then this relation is not a function. State the and of the following relation. s the relation a function? {(3, 5), (2, 5), (1, 5), (0, 5), (1, 5), (2, 5)} 'll just list the values for the and the values for the : : {3, 2, 1,0, 1, 2} : {5} r~nge _3~_6 This is a function. You can tell b tracing from each to each. There is onl one for each ; there is onl one arrow coming from each. o ~ Ha! Bet fooled some of ou on this one! This is a function! There is onl one arrow coming from each ; there is onl one for each. t just so happens that it's '16 alwas the same for each, but it is onl that one. So this is a function; it's just an etremel boring function! ~~

2 lao 3 ~ o This one is not a function : there are two arrows coming from the number 1; the number 1 is associated with two different elements. This is not a function! The "Vertical Line Test" Looking at this function stuff graphicall, what if we had the relation that consists of a set containing just two points: {(2, 3), (2, 2)}? We alread know that this is not a function, since = 2 has two corresponding has two corresponding values. f we graph this relation, it looks like: J~..... Notice that ou can draw a vertical line through the two points, like this:..,.. J'" f ou can draw a vertical line that crosses the graph in more than one place, then the relation is not a function. Here are a couple eamples: This graph shows a function, because there is no vertical line that will cross this graph twice. This graph does not show a function, because an number of vertical lines will intersect this oval twice. For instance, the ais intersects (crosses) the line twice.

3 For each of the following cases, state whether the information describes a function. f so, state the and. _3~_ o Function: _ Function: _ Domain : Domain : _ 3~ 2 1 : 4 Function : ~~ Function : Range : _3~_ o Function: Domain : Function:

4 Part ) What is the and of the following relation? {(1,2),(2, 51),(1,3),(8,22), (9,51) } : : 2) What is the and of the following relation? {(5,6),(21, 51),(11,93),(81,202), (l9,51)} : : 3) What is the and of the following smbolic relation? {(X~, (~~, (~, ~), (?,), ( ~,~), (~, ), (~, )} : : Part 1) Which relations below are functions? Relation # { (,2), (4,51), (1,2), (8,51) } Relation #2 {(13,14), (13,5), (16,7), (18,13)} Relation #3 {(3,90), (4,54), (6,71), (8, 90) } 2) Which relations below are functions? Wh? Relation #1 { (3,4), (4,5), (6,7), (8,9) } Relation #2 { (3,4), (4,5), (6,7), (3,9) } Relation #3 { (3,4), (4,5), (0,0), (8,9) } Relation #4 { (8, 11), (34,5), (6,17), (8,19) } 3) Which relations below are functions? Wh? Relation #1 { (3,4), (4,5), (6,7), (3,9) } Relation #2 { (3,4), (4,5), (6,7), (5,4) } Relation #3 { (0,4), (4,5), (0,0), (8,9) } Relation #4 {(8, 11 ), (34,5), (6,17), (6,19)} 4) For the following relation to be a function, X cannot be what values? { (8, 11), (34,5), (6,17), (X,22) }

5 5) For the following relation to be a function, X cannot be what values? { (12, 13), (11, 22), (33,101), (X,22) } 6) For the following relation to be a function, X can not be what values? {(12,14), (13,5), (2,7), (X,13)} 7) For the following relation to be a function, X can not be what values? { (13,14), (12,5), (16,7), (X, 13) } Ale states that the relation below is not a function. Lillian sas that it is a function. Who is correct? Eplain our reasoning. Eplanation: Relation { (13,14), (12,5), (16,7), (13, 14), (2,33), (13, 14 } TEACHERS: Feel free to make copies of this worksheet for the sole purpose of use in our own classroom. ENJOY!!!

6 RELATONS AND FUNCTONS 2 A RELATON A FUNCTON is a correspondence between two variables. is a set of points. is a relation such that for each value in the Domain, there is eactl corresponding value in the Range. Vertical Line Test for a Function A vertical line can intersect the graph of a function in at most one point, or using an alternate form, f an vertical line intersects the graph at more than one point, then the graph is NOT the graph of a function. ~ : ~ : ~ : ~,, ~. 7 ~ :. ~ ; ~ : ~.. ~. 6 c 5 4 ~. 4 ~. 3 5 ~. 2 3 col ~ B 3 ( 5)2 + ( 3)2 = 4 Line Segment = 2 3 Function? Function? Function? Ran ge: = ( 2)2 5 = ( 2 )2 + 1 = 3\ + 2 Function? Function? Function?

7 Unit 2: Worksheet 2 Domain and Range Name Period n 1 7, give the and for each of the following, then determine whether it's a function. l. 2. {(9, 0), (0,9), (4, 5), (5, 4)} Function? Function? Ordered Pairs: Ordered Pairs: Function? Function? Function? Function? Function? Holt 14.1 p.692

8 What Did the Bab Porcupine Sa ) When t Backed nto a Cactus? Determine which of the relations below are functions. Find the number of each relation that is a function at the bottom of the page and cross out the letter below it. When~ou finish. the answer to the title question will remain. c~~" CD {( 2, 7), ( 1, 5), (0, 3), (1, 1), (2, 1)}.. 7~ {(7, 20), (3, 5), (0, 5), (2, 0), (6, 4), (6, 9), (4, 4)} {(4, 8), (3, 2), (9, 6), (2, 1), (4, 5), (2, 7), (8, ).... ALGEBRA WTH PZZAZZ! OBJ~TVE 1a: To determine whetheror not a relation is a function. Creative Publications 175

9 u", l,;ul\i worksheet ALGEBRA Relations and Functions Name: Period: s each rel ation a function? Use a mapping diagram. E plain our an swer. 1. {(4, 7), (9, 11), (4, 6), (10, 2)} 2. {(5, 8), (2, 4). (3, 4), (6, 8)} s it a function? Eplain: :, 0, s it a function? Eplain: dentif which of the follo wing graphs are NOT functions. Answer(s):. (there ma be more than one!) 3. [A] [8 ] ,......,... ' " ,., ::: : : : :tq.,..,., " 0' : :: : :: :: :, :: : ::: :: : :.. 0 ' :: ::. ~,. [C] [D] s each relation a function? Use the vertical line test. Eplain our answer. 4. {(2, 5), (3, 5), (0, 5), (3, 5)} 5. {(, 9), (1, 3), (, 9), (6, 6)} r ', "'rr,r r : 'r : f L _.. _. L l l. oo!_l_.. o r+ i i [', " T, " n ~! i,! i i + ± _._ X 11~ 1 _. T 1... t. 1! 'r f.